This study will evaluate the safety and effectiveness of adding the experimental drug adefovir dipivoxil to lamivudine for treating hepatitis B virus (HBV) infection in HIV-infected patients with liver cirrhosis. Adefovir inhibits HBV by interfering with replication of the virus's genetic material. In some people, the drug has been active against strains of HBV that are resistant to lamivudine; it may also have some activity against HIV.